Analysis of Radiative Transport in a 2-D Cylindrical Participating Medium Subjected to Collimated Radiation

This article deals with the numerical analysis of radiative transport in a 2-D axisymmetric cylindrical enclosure containing absorbing, emitting, and scattering medium. The participating medium receives collimated radiation from the top boundary of the enclosure. Attenuation of the collimated radiation in the medium gives rise to the diffuse radiation. Thus, the governing radiative transfer equation accounts for both collimated and diffuse radiation. The radiative transfer equation is solved using the modified discrete ordinate method. Effects of extinction coefficient, scattering albedo, and aspect ratio on radial and axial distributions of heat flux and incident radiation are studied. In all cases, results are validated against those available in the literature. Modified discrete ordinate method has been found to provide accurate results.     

Thermal radiation in layered participating cylindrical media using an integral equation method

Radiative transfer in a layered cylindrical medium is analyzed using a newly developed S-type integral equation of transfer in terms of incident radiation and net radiative heat flux. The physical systems in hollow and solid cylindrical geometry are modeled as nonhomogeneous participating media with stepwise variable properties. Thus, the necessity to establish the equation of transfer for each layer and combine these layers through the intensity continuity on interface is avoided. Numerical predictions from a collocation method are presented to illustrate the effects of radiation properties on the radiative transfer for the systems considered. Comparison of the results with other available data in literature shows that highly accurate results are obtainable by current method with simplicity.     

Transient Prediction of Radiation Response in a 3-D Scattering-Absorbing Medium Subjected to a Collimated Short Square Pulse Train

Transient radiative transfer characteristics in a three-dimensional scattering-absorbing medium subjected to collimated irradiation of a short pulse train were investigated. A basic problem in which a cube is exposed to collimated irradiation of a single unit step square pulse was solved via the transient discrete-ordinates method, and Duhamel's superposition theorem was used to construct the responses of various pulse trains. The effects of optical thickness, scattering albedo, pulse width, and pulse train interval between two successive pulses on the temporal profiles of divergence of radiative heat flux, reflectance, and transmittance were scrutinized.     

Development and comparison of the DTM,the DOM and the FVM formulations for the short-pulse laser transport through a participating medium

The present article deals with the analysis of transient radiative transfer caused by a short-pulse laser irradiation on a participating medium. A general formulation of the governing transient radiative transfer equation applicable to a 3-D Cartesian enclosure has been presented. To solve the transient radiative transfer equation, formulations have been presented for the three commonly used methods in the study of radiative heat transfer, viz., the discrete transfer method, the discrete ordinate method and the finite volume method. To show the uniformity in the formulations in the three methods, the intensity directions and the angular quadrature schemes for computing the incident radiation and heat flux have been taken the same. To validate the formulations and to compare the performance of the three methods, effect of a square short-pulse laser having pulse-width of the order of a femtosecond on transmittance and reflectance signals in case of an absorbing and scattering planar layer has been studied. Effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor and the laser properties such as the pulse-width and the angle of incidence on the transmittance and the reflectance signals have been compared. In all the cases, results of the three methods were found to compare very well with each other. Computationally, the discrete ordinate method was found to be the most efficient.     

Modeling of coupled spectral radiation,thermal and carrier transport in a silicon photovoltaic cell

Photovoltaic conversion efficiency of a crystalline silicon cell is investigated as a function of its temperature and taking into account complete thermal and irradiation operating conditions. The spectral radiative transfer problem is solved through a gray per band approach and a separated treatment of the collimated and diffuse components of radiation fluxes. The heat transfer modeling includes local heat sources due to radiation absorption and thermal emission, non-radiative recombinations and excess power release of photogenerated carriers. Continuity equations for minority carriers are solved to provide the current–voltage characteristic. A detailed analysis of the electrical and thermal behaviors demonstrates that proper adjustment and control of both thermal and surroundings radiative operating conditions are likely to provide guidelines for the improvement of photovoltaic cell performances.     

Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

ABSTRACT

This paper presents a Chebyshev collocation spectral domain decomposition method (CSDDM) to study the coupled conductive and radiative heat transfer in a 3D L-shaped enclosure. The partitioned 3D L-shaped enclosure is subdivided into rectangular subdomains based on the concept of domain decomposition. The radiative transfer equation is angularly discretized by the discrete ordinate method with the SRAP_N quadrature scheme and then solved by the CSDDM using the same grid system as in solving the conduction. The effects of the conduction–radiation parameter, the optical thickness, the scattering albedo, and the aspect ratio on thermal behavior of the system are investigated. The results indicate that the 3D CSDDM has a good accuracy and can be considered as a good alternative approach for the solution of the coupled conduction and radiation problems in 3D partitioned domains.     

Combined non-gray radiative and conductive heat transfer in solar collector glass cover

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM).This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.     

燃烧室内三维温度场的辐射反问题

本文提出了一种在介质辐射特性已知的条件下,由壁面入射辐射热流的测量值反演燃烧室内三维温度场的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对吸收系数、散射不对称因子、反照率、壁面黑度和燃烧室大小尺寸等参数对反演精度影响的分析,结果表明,即使存在随机测量误差,这些参数对温度场反演精度的影响也不大,本文所提出的方法可较精确地反演燃烧室内三维温度场。     

Combined nongray radiative and conductive heat transfer in multiple glazing taking into account specular reflection and absorption

The problem of combined nongray radiative and conductive heat transfer in multiple glazing subjected to solar irradiation is analyzed. A spectral solar model proposed by Bird and Riordan is used to calculate direct and diffuse solar irradiance. The radiation element method by ray emission model, REM², is used to analyze the spectral dependence of radiative heat transfer. Specular reflection at boundary surfaces is taken into account. The spectral dependence of radiation properties of glass such as specular reflectivity, refraction angle, and absorption coefficient is taken into account. The steady‐state temperature and heat flux distributions in the glass layer are obtained and the insulating efficiency of multiple glazing is examined. The overall heat transfer coefficients predicted by the present method are compared with those based on the JIS method. The values obtained by the present method are slightly lower than those obtained by the JIS method. To investigate the spectral variation of radiative heat flux attenuated in the glass layer, the spectral heat flux at the room‐side surface and incident radiation are compared. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(8): 712–726, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10125     

Inverse Boundary Design Problems in Enclosures With Non-Gray Media

In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.     

Lattice Boltzmann simulations of a radiatively participating fluid in Rayleigh–Benard convection

Thermal radiation is an integral part of the heat transfer process but it is often neglected due to the complexity involved in the analysis of radiative transfer. We use the lattice Boltzmann method as a common computational tool to solve all three modes of heat transfer: conduction, convection, and radiation. This tool is then used to analyze the effect of radiatively participating medium on Rayleigh–Benard convection. We find that increasing the effects of radiation (i) increases the critical Rayleigh number required for the onset of Rayleigh–Benard convection and (ii) affects the temperature and flow patterns of convection rolls significantly changing the net heat transfer between the hot and cold plates. Both these effects are due to the presence of radiation available as an additional mode of heat transfer. Thus, we establish that the unified lattice Boltzmann framework is an effective computational tool for heat transfer and propose to use this method for a large range of problems in science and engineering involving radiative heat transfer.     

Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media

Radiative heat transfer in three-dimensional nonhomogeneous participating medium was investigated by using REM² method. The anisotropic scattering phase function was dealt with the scaling technique based on delta function approximation. The three-dimensional scaled isotropic results were compared with the published anisotropic scattering computations. A good agreement between the scaled isotropic approaches and the anisotropic solutions was found. The effects of scattering albedo, forward fraction of phase function, and wall emissivity were discussed. It was found that, with the increase of the scattering albedo, the radiative heat flux increases for forward scattering media, but decreases for backward scattering media. The radiative heat flux is increased with the increases of forward fraction of phase function and wall emissivity. The emissive power at the center of a cubical nonhomogeneous medium in radiative equilibrium with gray diffuse walls equals to the averaged blackbody emissive power of the six walls.     

On the discrete ordinates method for radiative heat transfer in anisotropically scattering media

In the discrete ordinates method (DOM), the normalized condition for the numerical quadrature of some complex scattering phase functions may not be satisfied. In this paper, a revised discrete ordinates method (RDOM) is developed to overcome this problem, in which a renormalizing factor is added into the numerical quadrature of in-scattering term. The RDOM is used to solve the radiative transfer problem in one-dimensional anisotropically scattering media with complex phase function. The radiative heat fluxes obtained by the RDOM are compared with those obtained by the conventional discrete ordinates method (CDOM) and Monte Carlo method. The results show the RDOM can overcome the false scattering resulted from the numerical quadrature of in-scattering term and improve largely the accuracy of solution of the radiative transfer equation by comparison with the CDOM.     

A Comparison of Angular Discretization Strategies for Modeling Radiative Transfer in Pool Fire Simulations

Decoupled radiative heat transfer calculations of 30-cm-diameter heptane pool fire are carried out employing the P1, discrete ordinates (DO), and finite-volume (FV) methods. The DO calculations are performed employing three different quadrature schemes (level symmetric hybrid [LSH], spherical surface symmetrical equal dividing angular quadrature [SSD], and TN). By scaling the soot field in the fire, the performances of the various methods are evaluated at different optical thicknesses by employing highly angularly resolved FV calculations (512 directions) as a reference. Twenty-four angular directions in the DO and FV methods are seen to be adequate to accurately predict the distributions of the divergence of the radiative flux within the fire. The corresponding accuracies of the P1 model are seen to decrease with increase in optical thickness. In the regions away from the fire, the P1 model performs poorly in predicting the axial as well as the radial radiative fluxes, whereas the errors associated with employing coarse angular resolutions in the DO method are seen to increase with soot concentrations and distance from the pool centre. Among the DO and FV models, the accuracies of the axial and radial incident radiative flux predictions outside the fire were more dependent on the angular resolution of the calculations rather than on the particular quadrature set employed in the calculations.     

RADIATION ELEMENT METHOD FOR TRANSIENT HYPERBOLIC RADIATIVE TRANSFER IN PLANE-PARALLEL INHOMOGENEOUS MEDIA

In this study the radiation element method is formulated to solve transient radiative transfer with light radiation propagation effect in scattering, absorbing, and emitting media with inhomogeneous property. The accuracy of the method is verified by good agreement between the present calculations and Monte Carlo simulations. The sensitivity of the method against element size, ray emission number, and time increment size is examined. The transient effect of radiation propagation is essential in short-pulse laser radiation transport when the input pulse width is not considerably larger than the system radiation propagation time. The transient characteristics of radiative transfer are investigated in the media subject to collimated laser irradiation and/or diffuse irradiation withtemporal Gaussian and/or square profiles. The inhomogeneous profile of extinction coefficient of the medium affects strongly the transient radiative flux divergence inside the medium.     

Mixed convection heat transfer in inclined rectangular ducts with radiation effects

A numerical study was carried out to investigate the radiation effect on the characteristics of the mixed convection fluid flow and heat transfer in inclined ducts. The three-dimensional Navier–Stokes equations and energy equation are solved simultaneously with the vorticity–velocity method. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The effects of the thermal buoyancy and the radiative transfer on the distributions of the bulk fluid temperature, the friction factor and the Nusselt number are emphasized in detail. Results indicate that radiation effects have a considerable impact on the heat transfer and tend to reduce the thermal buoyancy effects. In addition, the development of the bulk fluid temperature is enhanced by the radiation effects.     

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

The study of mixed convection heat transfer in horizontal ducts with radiation effects has been numerically examined in detail. This work is primarily focused on the interaction of the thermal radiation with mixed convection for a gray fluid in rectangular horizontal ducts. The vorticity–velocity method is employed to solve the three-dimensional Navier–Stokes equations and energy equation simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The attention of the results is focused on the effects of thermal buoyancy and radiative transfer on the development of temperature, the friction factor and the Nusselt number. Results reveal that radiation effects have a considerable impact on the heat transfer and would reduce the thermal buoyancy effects. Besides, the development of temperature is accelerated by the radiation effects.     

SOLVING A THERMAL REGENERATOR MODEL USING IMPLICIT NEWTON-KRYLOV METHODS

Laser tissue welding and soldering with use of short laser pulses are proposed. The transient radiation heat transfer in the picosecond time scale is numerically investigated for the first time using the discrete ordinate method for cylindrical geometries. The numerical method developed incorporates the propagation of radiation with the speed of light. The temporal radiation fields of tissue cylinders under the irradiation of short laser pulses are obtained. The use of short laser pulses for tissue welding and soldering is found to have reduced thermal damage to the healthy tissue and improves the uniformity of heating in the tissue closure region in both the depth and radial directions. The addition of absorbing solders in tissue soldering results in a well-confined radiation energy deposition field in the proximity of the solder-stained region and lessens the outgoing radiative heat flux at the laser incident surface. Comparisons of radiation heat transfer are made between the spatially square-variance and Gaussian-variance laser inputs and between the temporally Gaussian-profile and skewed-profile pulses, respectively.     

改善材料选择性热辐射的方法

从波动力学的观点出发，解析了热辐射波和材料内部的阻尼谐振子之间的相互作用过程，从而揭示了热辐射波在材料内部的发射、吸收、透射和反射机理。基于洛伦兹色散理论，分析了影响材料选择性热辐射的因素，提出了改善材料选择性热辐射复合化和超细化方法。实验研究证实了这些方法的正确性和可靠性。